Engineering Transactions, 34, 4, pp. 531-542, 1986

A Note on Recent Developments in the Theory of Elastic Plates with Moderate Thickness

T. Lewiński
Technical University of Warsaw, Warszawa

The paper refers to Reddy's concept (Int. J. Solids Struct., 20, No 9/10, pp. 881-896, 1984) of a construction of the energy consistent theory for plates with moderate thickness; this theory is based on the kinematical hypothesis known from the monographs by Ambartsumian and Kączkowski. With the use of other. independent physical quantities. (we handle the averaged Reissner's rotations), the equations of motion and boundary conditions are derived. By means of simplifications of functionals, the governing equations and boundary conditions of the Reissner-type model (found by Kączkowski and then discovered again by Levinson) are arrived at. In the last section a proof is given that there is no simple generalization of the kinematical hypothesis used in the paper which would lead to an energy-consistent and physically correct theory of the Reissner class.

Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


E. REISSNER, On the theory of bending of elastic plates, J. Mathematics and Physics, 23, 184-191, 1944.

H. HENCKY, Uber die Berucksichtigung der Schubverzerrung in ebenen Platten, Ing. Archiv, 16, 72-76, 1947.

R. D. MINDLIN, Influence of rotatory inertia and shear on flexural vibrations of isotropic, elastic plates, J. Appl. Mech. 18, 31-38, 1951.

A. KROMM, Verallgemeinerte Theorie der Plattenstatik, Ing. Archiv. 21, 266-286, 1953. V. PANC, Verscharfte Theorie der elastischen Platte, Ing. Archiv, 33, 351-371, 1964.

С. А. АМБЛРЦУМЯН, Теория анизотронных пластин, Наука, Москва 1967.

И. Н. ВЕКУА, Теория тонких пологих оболочек переменной толщины, Мецниереба, Тбилиси 1965.

И. И. ВЕКУА, Некоторые общие методы построения различтtых вариантов meоpиu оболочек, Наука, Москва 1982.

Z. KĄCZKOWSKI, Płyty. Obliczenia statyczne, Arkady, Warszawa 1968 [second edition: 1980]. G. JEMIELITA, Techniczna teoria płyt średniej grubości, Rozpr. Inż., 23, 3, 483-499, 1975. V. PANC, Theories of elastic plates, Academia, Prague 1975. M. LEVINSON, An accurate simple theory of the statics and dynamics of elastic plates, Mech. Res. Comm. 7, 6, 343-350, 1980. J. N. REDDY, A refined nonlinear theory of plates with transverse shear deformation, Int. J. Solids. Structures, 20, 9/10, 881-896, 1984.